CGMO 2007 Problem 3

Let $n$ be an integer greater than $3$ , and let $a_1, a_2, \cdots, a_n$ be non-negative real numbers with $a_1 + a_2 + \cdots + a_n = 2$ . Determine the minimum value of $$\frac{a_1}{a_2^2 + 1}+ \frac{a_2}{a^2_3 + 1}+ \cdots + \frac{a_n}{a^2_1 + 1}.$$